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Power stabilization of a diode laser with an
acousto-optic modulator
F. Tricot, D. Phung, M. Lours, S. Guérandel, E. de Clercq
To cite this version:
F. Tricot, D. Phung, M. Lours, S. Guérandel, E. de Clercq. Power stabilization of a diode laser with
an acousto-optic modulator. Review of Scientific Instruments, American Institute of Physics, 2018,
89 (11), pp.113112. �10.1063/1.5046852�. �hal-01981700�
F. Tricot,1, 2, a) D. H. Phung,1M. Lours,1 S. Gu´erandel,1and E. de Clercq1
1)
LNE-SYRTE, Observatoire de Paris, Universit´e PSL, CNRS, Sorbonne Universit´e, 61 avenue de l’Observatoire, 75014 Paris, France.
2)Thales AVS, 2 rue Marcel Dassault, 78140 Velizy-Villacoublay, France.
Laser power fluctuations can significantly reduce the device performances in various applications. High fre-quency fluctuations impact the signal-to-noise ratio, while slow variations can reduce the device repeatability or accuracy. Here we report experimental investigations on the power stabilization of a diode laser with an acousto-optic modulator. In the frequency domain the relative power noise is reduced at the level of
2.2 × 10−8 Hz−1/2 in the range 1-100 kHz. The slow variations are studied in the time domain. The relative
Allan standard deviation is measured at the level of 6 × 10−7 at 100 s averaging time. Above 100 s the
instability increases and reaches 2 × 10−6 at 10 000 s.
I. INTRODUCTION
Stable laser powers are needed in a wide range of
appli-cations such as laser writing systems1, magnetometers2,
atomic clocks3–5, spectroscopy6–9, laser frequency
standards, interferometry and gravitational wave
detection10,11, etc. High frequency fluctuations of laser
power decreases the signal-to-noise ratio, degrading the
short-term frequency stability of frequency standards5,
or can distort line-shapes in frequency modulation
spectroscopy7. Low frequency variations can degrade
long-term stability of atomic clocks4,5. Various
ap-proaches can be employed to tackle this issue. Aside
from passive isolation12, the optical power can be
stabi-lized by a feedback on the diode current (at the expense
of the frequency stability) or temperature13. Most often
an external actuator is used for this purpose, like an
electro-optic modulator14,15, a photo-elastic modulator2,
or an acousto-optic modulator (AOM)1,3,8–11,16,17. A
great deal of work has been devoted for decades to the AC power stabilization of Nd:YAG lasers for
gravita-tional wave detectors. A relative power noise (RPN)
at the outstanding level of 1.8 × 10−9 Hz−1/2 in the
100 Hz-1 kHz band has recently been demonstrated11
with AOM. However these highly sophisticated devices are too complex for industrial applications or ordinary laboratories, and cannot be implemented in on-board devices such as compact atomic clocks which must
be small and low-power. Although the laser-power
stabilization by means of an AOM is well known and very common in many laboratories, surprisingly, it is very poorly documented in the literature. Particularly the slow power fluctuations and drifts are not addressed. The aim of this paper is to fully describe and charac-terize a simple and efficient setup for on-board applica-tions or ordinary laboratories, so that it could be used as a guideline. The limiting noise sources of the device and of the measurement are carefully addressed. The device performances are characterized in the frequency domain (power spectral density (PSD) in 1 Hz-10 MHz
a)francois.tricot@obspm.fr
band) and in time domain (very slow frequencies, averag-ing times from 1 s to 10 000 s). They are investigated by means of the Allan standard deviation, which character-izes the power instability as a function of the averaging time. RPN and Allan deviation both allow an analysis of the limiting noise types, but in frequency domain and time domain, respectively. The link between noise power spectral density and Allan deviation, well known in time
and frequency metrology18, will be used to confirm the
analysis.
In this paper we characterize the power stabilization of a diode laser based on a simple scheme using a sin-gle acousto-optic modulator (AOM). This is needed for a project of compact vapor-cell atomic clock based on coherent population trapping. Vapor cell atomic clocks
based on coherent population trapping (CPT)19–22 are
promising devices for their potential compact size23 or
their high performances5,24–26. In such clocks there is
no microwave cavity unlike well-known Rb vapor cell
clocks27, the microwave signal is optically carried by a
bi-frequency laser beam. The CPT clock resonance occurs when the frequency difference between both optical fre-quencies is equal to the microwave clock frequency. The resonance is detected by recording the optical power of the light transmitted through the vapor cell. The coun-terpart of this all-optical interrogation and detection is the high sensitivity to the laser power. The signal ampli-tude and the clock frequency are both power sensitive.
In our setup the two frequencies are produced by two
home-made extended-cavity diode lasers (ECDL)28. One
laser is frequency stabilized by saturated absorption spec-troscopy on the Cs D1 line at 895 nm. The slow fre-quency corrections are applied on a piezoelectric trans-ducer (PZT) controlling the cavity length, while fast cor-rections are applied on the diode driving current. Such actions, cavity-length and current variations, in turn modify the output power and alter the power stability. The PSD of the relative power noise (RPN, also called RIN in the literature) of a diode laser is shown in Fig. 1. As expected the noise spectrum of the free-running laser is dominated by flicker noise. The laser frequency locking adds two supplementary noise peaks on the spec-trum, related to the PZT and diode current at low and high frequency, respectively.
2 1 1 0 1 0 0 1 k 1 0 k 1 0 0 k 1 M 1 0 M - 1 5 0 - 1 4 0 - 1 3 0 - 1 2 0 - 1 1 0 - 1 0 0 - 9 0
( 1 )
( 2 )
RP N [d B/ H z] f [ H z ]FIG. 1. Relative power noise of the ECDL laser. (1) Free running; (2) the laser frequency is locked on the Cs D1 tran-sition.
Since the laser power fluctuations are one of the main sources of frequency instability in our clock, we imple-mented a simple low noise power lock for each laser based on AOMs. Fast fluctuations affect the short-term fre-quency instability, and are characterized by the RPN. Slow power variations are one of the major source of in-stability at midterm averaging times. They are investi-gated by means of the Allan standard deviation.
The paper is organized as follows. We first describe the experimental set-up controlling the laser power and the servo electronic circuit. The results on the RPN re-duction, in loop and out-of-loop, are then presented. The last part is devoted to the analysis and reduction of the slow power fluctuations.
II. POWER SERVO
A schematic of the setup used for power locking is
shown in Fig. 2. The laser beam passes through an
AOM (Crystal Technology 3080) in the Bragg configu-ration. The AOM position is set to optimize the first-order diffraction beam thanks to a xy dual-axis transla-tion stage and a θ rotatransla-tion mount (Fig. 2). The first-order beam is blocked further away. Usually, a part of the zero-order beam is picked up by using a beamsplit-ter of split ratio 10/90 or 30/70. For this experiment, the beamsplitter is replaced by an half-wave plate and a polarizing cube (PBS) to get a variable split ratio.
The transmitted beam is the useful beam, its power Pout
is monitored by a photodiode PDo (out-of-loop signal),
the reflected beam power (Pin) is detected by an
iden-tical photodiode PDi (Thorlabs-PDA36A), yielding the
in-loop signal. The optical bench is enclosed in a box whose temperature stability is of several tens of mK.
The in-loop signal is compared to a reference voltage issued from a low noise and low drift precision voltage reference (Linear Technology, LT1021-10V). The error
FIG. 2. Experimental set-up stabilizing the laser power. The power lock controls the level of the RF signal. AOM acousto-optic modulator, λ/2 half-wave plate, PBS polarizing beam splitter, Vref voltage reference, PDi (PDo) in-loop
(out-of-loop) photodiode, respectively .
signal, difference between the photodiode signal and the reference, is integrated through a proportional-integrator controller (PI). The correction is applied on an attenua-tor (Mini-Circuit, TFAS-2+) controlling the power level of the 80 MHz radio-frequency (RF) signal driving the AOM, i.e. the servo controls the power balance between AOM diffraction orders. The control efficiency is charac-terized in the frequency domain by the noise PSD. For Fourier frequency above 1 Hz the noise spectra of the various signals are recorded by a fast-Fourier-transform analyzer (FFT, Agilent-89410A). In the time domain, for averaging time above 1 s, the slow variations are charac-terized by the Allan standard deviation. A data acquisi-tion unit (Agilent 34970) is used for time measurements of the laser power.
FIG. 3. Power-lock circuit. LT1021, high-stability voltage reference. The OP amplifiers are MAX9632 except for the OP27 buffer b, f unity gain buffer amplifier, d differential amplifier, ng non-inverting gain amplifier, pi proportional-integrator controller, PDi in-loop photodiode.
The electronic diagram is shown in Fig. 3. Low-noise and wide-band operational amplifiers (OP) MAX9632 are used, except for the buffer amplifier (b). Two unity gain buffer amplifiers (f) isolate possible noise returns which would degrade the characteristics of the voltage reference. In addition, the second OP (f) is used to adjust the volt-age reference at the desired level. This adjustment is made by monitoring the error signal available with the
OP27 buffer (b). After a non-inverting gain amplifier (ng), the error signal is processed by a PI controller with a bandwidth of about 700 kHz. The optimal parameters to reduce the RPN laser close to the relative voltage ref-erence are founded to be R1 = 5 kΩ, R2 = 1 kΩ and C = 220 pF.
III. RELATIVE POWER NOISE A. In-loop power value
The laser power Pin used in the servo loop must be
high enough so that photodiode noise and shot noise are negligible. However, in our set-up the total power available at the output of the AOM is low, only about
7 mW. As the Pinvalue increases, the out-of-loop power
Pout decreases, so that its shot-noise increases in
rela-tive value.In this way the value of Pin minimizing the
in-loop noise, is not the value minimizing the out-of-loop noise floor. With the half-wave plate and the PBS we
experimented different values of Pin to reach the
low-est out-of-loop RPN floor. The experimental results are shown in Fig. 4. The out-of-loop RPN noise floor value is taken at 4 kHz Fourier frequency from the RPN mea-surements presented in the inset. The experimental data (squares) are in fairly good agreement with a simple
es-timation (solid line) given by RP Nout∼ REF + P Din+
P Dout+ SNin+ SNout, with REF the voltage-reference
noise PSD in relative unit, SNin and SNout the relative
shot-noise PSDs of the in-loop and out-of-loop signals,
respectively. P Dinand P Dout are the noise PSDs of the
photodiodes PDi and PDomeasured in the dark and
di-vided by the squared mean signal value.
At low Pin values, the power lock cannot efficiently
filter the laser noise because the in-loop noise is
domi-nated by the photodiode noise. When Pin is increased
above 4 mW, in order to reduce the in-loop photodiode noise contribution, the out-of-loop power is decreased. Therefore the out-of-loop RPN floor value is dominated by the shot-noise of the out-of-loop signal. In the
fol-lowing, Pin = 3 mW, this value is a good trade-off to
avoid the contribution of the in-loop detection noise and to keep enough power laser for the useful beam.
B. In-and out-of-loop results
The in-loop measurement of the RPN PSD is shown in Fig. 5, together with the noise PSDs of the voltage reference and of the photodiode. The voltage reference noise is measured after the differential amplifier (d) (Fig. 3). For purposes of comparison all PSD are normalized to the photodiode-signal mean value. When the servo-loop is closed, the RPN is reduced by 40 dB at 100 Hz
Fourier frequency. From 200 Hz to 60 kHz the noise
floor is close to the floor of the voltage reference at the level of −158.5 dB/Hz. The bump visible on the RPN
0 1 2 3 4 5 - 1 6 0 - 1 5 6 - 1 5 2 - 1 4 8 - 1 4 4 - 1 4 0 1 0 0 1 k 1 0 k - 1 5 5 - 1 5 0 - 1 4 5 - 1 4 0
R E F
P D i n
S N o u t
RP
N
ou
t f
lo
or
[d
B/
H
z]
P
i n[ m W ]
S N i n
P i n = 1 . 5 m W P i n = 3 . 5 m W RP N ou t [ dB /H z] f [ H z ] P i n = 0 . 5 5 m WFIG. 4. Noise floor value of the out-of-loop RPN as a function of the in-loop power laser Pin. Black squares experimental
data, blue solid line computed value. The floor value is the RPN level at 4 kHz Fourier frequency. REF, PDin, SNin, and SNout contributions of the voltage reference, in-loop photo-diode, in-loop and out-of-loop shot noises, respectively. The inset shows the out-of-loop RPN measured from 100 Hz to 50 kHz for three values of Pin.
1 1 0 1 0 0 1 k 1 0 k 1 0 0 k 1 M 1 0 M - 1 7 0 - 1 6 0 - 1 5 0 - 1 4 0 - 1 3 0 - 1 2 0 - 1 1 0 - 1 0 0
( 2 )
( 1 )
( 3 )
( 4 )
RP N [d B/ H z] f [ H z ]FIG. 5. In-loop RPN in free running (1) and power-locked (2) regimes. (3) Normalized voltage-reference noise, (4) pho-todiode noise.
curve around 600 kHz Fourier frequency does not exceed −144 dB/Hz. Above 2 MHz, the measurement is limited by the photodiode noise. This result shows that the servo loop can filter the laser-power noise in the loop at the level of the reference noise up to 100 kHz. The same result is obtained on both laser systems.
The out-of-loop RPN is shown in Fig. 6. When
the power servo-loop is locked the RPN level is about −147 dB/Hz at 100 Hz Fourier frequency, a reduction of about 32 dB compared to the unlocked power case. The noise floor level from 1 kHz to 100 kHz is limited by the
4 1 1 0 1 0 0 1 k 1 0 k 1 0 0 k 1 M 1 0 M - 1 6 0 - 1 5 0 - 1 4 0 - 1 3 0 - 1 2 0 - 1 1 0 - 1 0 0
( 2 )
( 3 )
( 1 )
RP N [d B/ H z] f [ H z ]FIG. 6. Out-of-loop RPN in free running (1) and power-locked (2) regimes. (3) Normalized voltage-reference noise. The dashed lines represent the asymptotic flicker noise at low frequency.
bump servo loop is visible around 500 kHz Fourier
fre-quency. The asymptotic behavior in h−1f−1of the flicker
noise at low Fourier frequencies f will help to understand the Allan deviation measurements in the next section.
We recall18 that a PSD of function h
−1f−1 (h0) leads to
an Allan deviation equals top2 ln(2)h−1(ph0/2τ−1/2),
respectively, where τ is the averaging time. For the
voltage reference and for the out-of-loop RPN we get:
h−1 = 6.3 × 10−15 (−142 dB) and h−1 = 2 × 10−13
(−127 dB), respectively.
This noise level leads to a reduction of the RPN con-tribution to the frequency instability of our CPT clock
at the level of 2.5×10−14 at 1 s averaging time instead of
5×10−13 when laser powers are not stabilized.
IV. SLOW POWER FLUCTUATIONS A. Data acquisition characterization.
Before investigating the slow power fluctuations we checked the possible contributions of the voltage suring instrument and of the voltage reference. We mea-sured the low-frequency fluctuations of the voltage refer-ence and of the laser power by using the data logger. As we needed to measure fractional laser-power fluctuations
below σP/P ∼ 1 × 10−6 at 10 000 s integration time, we
first characterized the data logger stability. This
instru-ment has a typical resolution of about 10µV for a 10 V
range. The result of a measurement of the null voltage of a short-circuit during more than 180 hours , is shown
in inset of Fig. 7. The measured resolution is RS = 11.2
µV. The measurement stability is characterized by the Allan standard deviation (Fig. 7) which is here divided by 10 V for purposes of comparison with further power
measurements in fractional units. The slope in τ−1/2,
with τ the averaging time, is the feature of a white noise.
The slope here is equal to (r/√2)τ−1/2, with r = RS/10.
This result shows that the data logger can measure
rel-FIG. 7. Allan deviation of the voltage noise measured on a short-circuit. The deviation is normalized to 10 V. Dots data, red line computed line of slopepr2/2τ−1/2
. The inset shows the measurement during 180 h.
ative fluctuations below 1×10−6 at 10 000 s averaging
time.
B. Voltage reference instability
We measured with the data logger the reference volt-age at various points of the power lock circuit (see inset of Fig. 8), (1) at the output of the LT1021 reference, (2) at the output of the differential amplifier with the
in-loop photodiode PDiin the dark. The measured relative
Allan deviations are shown in Fig. 8 up to 10 000 s aver-aging time. Note that the values are normalized to 10 V for curve (1), and 5 V for curve (2), which is the mean value in working conditions. The curve (2’) shows the measured instability with a previous version of the elec-tronic board using common resistors (temperature sen-sitivity 5 ppm/K) instead of low temperature coefficient (Vishay) resistors (0.05 ppm/K).
At short term (τ < 100 s) the measurement of the LT1021 instability (curve (1)) is limited by the data
logger noise. The LT1021 flicker noise (see Fig. 6)
yields indeed a relative Allan deviation floor of about
p2 ln(2)h−1= 1 × 10−7, well below the data logger
de-viation. The voltage reference floor is reached between 100 and 1 000 s averaging times.
The instability begins to increase above 1 000 s. The instability of the reference voltage measured after the differential amplifier (curve (2)) has the same behavior. The factor of 2 compared to curve (1) is due to the dif-ferent dividing values (5 V and 10 V) for the same noise value. In the following the power instability will be
com-FIG. 8. Allan deviation of the relative voltage reference mea-sured at (1) LT1021 output (10 V), and (2) after the differ-ential amplifier (5 V) with electronic board using low tem-perature coefficient resistors or common resistors (2’). The dashed line represent the expected results by summing only contributions of data-logger white noise and LT1021 flicker noise. The inset scheme shows where the measurements are performed.
pared to the minimum measurable instability given by
σ2(τ ) = (r2/2)τ−1+ 2 ln(2)h
−1.
C. Laser Power instability
The measured laser-power instability of a single laser is shown in Fig. 9. When the power loop is closed, the instability (2) is one order of magnitude lower than for free-running regime (1). According to the flicker noise level in Fig. 6, at short averaging times the closed-loop
instability should be 5.3 × 10−7. We cannot measure this
level masked by the data logger instability. At 1 s aver-aging time the instability is closed to the expected value (5) computed by summing theoretical contributions of data logger and RPN. However, after 1 s, the instability
increases and reaches 9×10−5 at 10 000 s. The Allan
de-viation scales as τ , which is consistent with a linear drift. This drift cannot be explained by the voltage reference whose contribution is here negligible (see Fig. 8).
Actually, the power variations of Poutare correlated to
the temperature variations in the box enclosing the ex-perimental set-up. We identified the AOM as one of the
main temperature sensitive component (∼ 10−2/K). The
AOM crystal is a tellurium dioxide (TeO2 or
paratellu-rite) crystal, known to be highly birefringent29–31. Then
if the incident polarization is not perfectly linear and aligned on one crystal axis the output polarization will
1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 - 7 1 0 - 6 1 0 - 5 1 0 - 4 1 0 - 3
( 4 )
( 3 )
( 5 )
( 1 )
( 2 )
σ
p/P
(
τ
)
τ
[ s ]
FIG. 9. Relative laser-power instability. (1) Free-running power, (2) power-locked regime without AOM temperature regulation, (3) power-locked regime with AOM temperature regulated at 27.8◦C, (4) power-locked regime with AOM tem-perature regulated at 27.8◦C, and with the use of an uncoated BS to pick up the laser beam, (5) expected instability.
be rotated or its ellipticity will change, and this effect
is temperature sensitive. To characterise it, we have
recorded the powers Pin and Pout as a function of the
AOM temperature, regulated by a thermo-electric cooler (TEC) placed under it. The inset in figure 10 shows the powers measured at the output of the PBS for the hor-izontal and the vertical polarizations. The beam at the input of the AOM is linearly and vertically polarized, and the half-wave plate in-front of the PBS is removed. The vertical polarization is the polarization recommended by the manufacturer for the best diffraction efficiency. A polarization modulation is clearly observed. Note that the same modulation is observed with the horizontal
po-larization with a smaller amplitude. Figure 10 shows
the normalized in-and-out-loop powers around 28◦C in
working conditions (the plate is in front of the PBS, and
tilted for tuning the split ratio). Pin(Pout) is the power
of the vertically (horizontally) polarized output beam, respectively. It is clear that the AOM is sensitive to tem-perature variation, in such a way that the AOM crystal changes the polarization of the output laser beam before the PBS. Consequently, when the power loop is closed, a
temperature variation leads to opposite variation of Pin
and Pout. The servo regulates Pin to a constant value
by correcting the total power by means of the RF power
driving the AOM, and so the Pinlock increases the
vari-ation of Pout.
An interesting point to be noticed is the AOM
tem-perature sensitivity around 27.8 ◦C, which shows an
inversion temperature (Fig. 10). To confirm this
ef-fect, we measured the power instability out of the loop
while the AOM temperature is regulated at 27.8◦C by
6 2 6 . 4 2 6 . 8 2 7 . 2 2 7 . 6 2 8 . 0 2 8 . 4 2 8 . 8 0 . 9 9 1 . 0 0 1 . 0 1 1 . 0 2 1 . 0 3 1 5 2 0 2 5 3 0 3 5 4 0 0 . 0 0 . 1 0 . 2 7 . 8 7 . 9 8 . 0 P v P h P t
P i n
N or m ali ze d Po we r T A O M [ ° C ]P o u t
P [ar b. u ni t] ° CFIG. 10. Normalised optical powers measured in and out of the loop as a function of the AOM temperature. Each power is normalized to its mean value at 27.8◦C. The data scattering is due to back and forth scans. Inset: Powers measured at the PBS output for a linearly or vertically polarized beam at the AOM input. Ph: horizontal polarization, Pv: vertical polarization, Pt: sum of Ph and Pv powers.
result is shown in Fig. 9(3). We clearly see an improve-ment of the stability, now equal to the expected value (5) until 100 s. Between 100 and 10 000 s an improvement of a factor close to five is obtained. This result confirms the AOM temperature influence on the power instability. Nevertheless, a power drift is still visible above 500 s. The Allan deviation of the regulated AOM temperature
is 6 × 10−5 ◦C and 1 × 10−3 ◦C at averaging times of 100
and 10 000 s, respectively. These values lead to fractional
out-of-loop power deviations of 4 × 10−8 and 6 × 10−7.
The remaining power drift is then not due to the AOM sensitivity. In order to overcome the birefringent effect in the AOM, we inserted a polarizer between the AOM and the half-wave plate, so that the polarization does not change at the input of the plate. This did not re-duce the observed power drift. As a matter of fact, the residual thermal contribution is due to the use of the half-wave plate and the PBS, which was used to tune the beam part extracted for the servo-loop. Its sensitivity
has been measured to be about ≤ 8 × 10−3/K. We have
then replaced the plate-PBS set by an uncoated glass plate. As seen in section III A the in-loop power is no more optimized for PSD floor, but here the purpose is to check the impact on long term variations. The resulting relative power instability is shown in Fig. 9. An improve-ment of a factor six is obtained at 10 000 s, at the level of
2.5×10−6(Fig. 9(4)). The residual power drift measured
from 1 000 s to 10 000 s is attributed to temperature
sen-sitivity of both photodiodes (∼ 2×10−4/K). Note that
the beam pointing stability after an AOM is also
sensi-tive to the RF power32. Here the fractional fluctuations
of the RF power is less than 10−3 leading to an angular
stability below 1µrad with data of Ref.32. As the active
area of the photodiodes is 13 mm2 we can neglect such
an angular variation.
V. CONCLUSION
We have reported the characterization of a simple
AOM-based power lock for a diode laser. The
“high-frequency” power fluctuations are investigated in the fre-quency domain by the RPN for Fourrier frequencies be-tween 1 Hz and 1 MHz. The power flicker noise is reduced by 32 dB until 100 Hz Fourier frequency. This noise level leads to a reduction of the RPN contribution to the clock frequency instability at 1 s averaging time at the level of
2.5×10−14 instead of 5×10−13when laser powers are not
stabilized.
The slow fluctuations are studied in the time domain by means of the Allan deviation for averaging times be-tween 1 s and 10 000 s. The measurement is limited by the instrumentation at short averaging times τ . A
minimum at the level of 5 − 6 × 10−7 is obtained from
τ = 200 s to τ = 1 000 s. At longer times the instabil-ity increases, related to a power drift. A first drift was explained by temperature sensitive birefringent effects in the AOM. The second drift is due to the temperature sensitivity of the half-wave plate combined with a PBS. This component must be replaced, as far as possible, by a polarization-and temperature insensitive beamsplitter. The residual drift is probably due to thermal photo-diode sensitivity. Nevertheless, the power instability reaches
now the 2×10−6 level at τ = 10 000 s, i.e. a
reduc-tion by almost three orders of magnitude by respect to the free running case. It is worth to note that such a power instability could still be limiting for a CPT clock
based on a continuous interrogation25, but not for a clock
based on a Ramsey interrogation thanks to a new
tech-nique known as autobalanced Ramsey spectroscopy33,34
which can dramatically reduce laser-power effect on the
frequency in CPT-Ramsey clocks35,36. Finally, we have
shown that a high power stability can be reached with a simple device based on a single AOM. Such a report can be useful in many laboratories working in various fields like atomic physics, optics, sensors, or metrology, in or-der to know what results can be achieved in frequency and time domains with this scheme, and what are the issues.
ACKNOWLEDGMENT
We are grateful to Jos´e Pinto Fernandes for his skill in
electronics and his patience. We thank P. Yun, R. Bouc-hand, and Y. Le Coq for valuable contributions. We also thank V. Giordano and F. Du Burck for helpful com-ments. We are indebted to R. Boudot for valuable dis-cussions and careful reading of the manuscript. F. T.
was supported by French MoD, Direction G´en´erale de
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